Figures (8)  Tables (6)

    • Figure 1. 

      MOCP-RVTO instruction on roads.

    • Figure 2. 

      GAD-based MOCP-RVTO solving approach execution flow diagram.

    • Figure 3. 

      Sioux Falls example network structure.

    • Figure 4. 

      Z-based fitting curves. (a) ds = 60. (b) ds = 120. (c) ds = 180. (d) ds = 240.

    • Figure 5. 

      Objective function values based on different optimal objectives. (a) ds = 30. (b) ds = 60. (c) ds = 90. (d) ds = 120. (e) ds = 150. (f) ds = 180. (g) ds = 210. (h) ds = 240. The unit of Z1 value is 100, the unit of Z2 value is 10,000, the unit of Z3 value is also 100, and the unit of |L| value is 1.

    • Figure 6. 

      Total rescue vehicle traffic volumes assigned to roads. (a) Max Z1. (b) Min Z2. (c) Min Z3. (d) Min Z.

    • Figure 7. 

      Sioux Falls Paramics social vehicle traffic simulation network.

    • Figure 8. 

      Number of social vehicles.

    • Objective index Route index
      A B C
      Traffic efficiency L M H
      Traffic distance L M H
      Traffic distribution L M H
      H, M, and L represent the high, medium, and low levels, respectively.

      Table 1. 

      Traffic route characteristics.

    • Notations Definitions
      Sets
      $ L $ Set of links that constituting the rescue vehicle traffic network
      $ L' $ Set of links where rescue vehicles enter the disaster position from the road network, $ L'\subset L $
      $ L'' $ Set of links where rescue vehicles enter the road network from the rescue station, $ L''\subset L $
      $ S $ Set of rescue stations
      $ \Gamma _{i}^{+} $ Set of links that connect with link i in its downstream direction,$ i\in L,\Gamma _{i}^{+}\subset L $
      $ \Gamma _{i}^{-} $ Set of links that connect with link i in its upstream direction,$ i\in L,\Gamma _{i}^{-}\subset L $
      $ T $ Set of integer time periods that describe the dynamic rescue vehicle traffic network loading process
      Indices
      $ i,j $ Index of any link on the road network, $ i,j\in L $
      $ t,\tau $ Index of any time period, $ t,\tau \in T $
      $ s $ Index of any rescue station, $ s\in S $
      $ o $ Index of the disaster position
      Parameters
      $ \alpha ,\delta $ Linear interpolation coefficient of cumulative traffic volume in non-integer time periods
      $ {d}_{s} $ Rescue traffic demand that represents the number of rescue vehicles called from rescue station$ s $, $ s\in S $
      $ {l}_{i} $ Length of link i, $ i\in L $
      $ {n}_{i} $ Number of lanes of link i, $ i\in L $
      $ {Q}_{i} $ Road capacity, that is, the maximum number of rescue vehicles that can pass every lane of link i within any time period t, $ t\in T,i\in L $
      $ \rho _{jam}^{(i)} $ Jam traffic density, that is, the maximum number of rescue vehicles that can be accommodated on every lane of link i, $ i\in L $
      $ {\tau }_{i} $ Length of traffic free-flow time periods from upstream end to downstream on link i, $ i\in L $
      $ {\iota }_{i} $ Length of backward traffic congestion shockwave propagation time periods from downstream end to upstream on link i, $ i\in L $
      Variables
      $ U_{t}^{(i)} $ Cumulative number of rescue vehicles entering link i by the end of current time period t, $ t\in T,i\in L $
      $ V_{t}^{(i)} $ Cumulative number of rescue vehicles leaving link i by the end of current time period t, $ t\in T,i\in L $
      $ q_{t}^{(i,j)} $ Number of rescue vehicles entering link j from link i within current time period t, $ t\in T,i\in L,j\in \Gamma _{i}^{+} $
      $ q_{t}^{(i,o)} $ Number of rescue vehicles arriving in the disaster position o from link i within current time period t, $ t\in T,i\in L' $
      $ q_{t}^{(s,i)} $ Number of rescue vehicles entering link i from rescue station s within current time period t, $ t\in T,i\in L'',s\in S $
      $ x_{t}^{(i)} $ Number of rescue vehicles on link i in the beginning of current time period t, $ t\in T,i\in L $

      Table 2. 

      Formulation notations and definitions.

    • Link indexNode seriesLanesLength (m)Link indexNode indexLanesLength (m)Link indexNode indexLanesLength (m)
      11→249002710→1123005317→191200
      21→342002810→1524005418→74200
      32→129002910→1613005518→163300
      42→612003010→1713605618→204855
      53→122003111→414005719→153300
      63→433003211→1023005819→171200
      73→1244003311→1213005919→201400
      84→333003411→1414006020→184855
      94→533003512→344006120→191400
      104→1114003612→1113006220→211300
      115→433003712→1348006320→221360
      125→613003813→1248006421→201300
      135→922003913→2413006521→221200
      146→212004014→1114006621→241300
      156→513004115→1413006722→152200
      166→812004214→2312006822→201360
      177→813004315→1024006922→211200
      187→1842004414→1513007023→221300
      198→612004515→1933007123→141200
      208→713004615→2222007222→231300
      218→913004716→812007323→241200
      228→1612004816→1013007424→131300
      239→522004916→1712007524→211300
      249→813005016→1833007624→231200
      259→1022005117→101360
      2610→922005217→161200

      Table 3. 

      Traffic network attributes.

    • Weightds = 30ds = 60ds = 90ds = 120ds = 150ds = 180ds = 210ds = 240
      a10.99180.99180.99180.99180.98970.99180.99180.9918
      a20.00500.00500.00500.00500.00700.00500.00500.0050
      a30.00320.00320.00320.00320.00330.00320.00320.0032

      Table 4. 

      Objective weight optimization results.

    • ObjectivesCombination weights (a1, a2, a3)
      (0.9918, 0.0050, 0.0032)(0.9897, 0.0070, 0.0033)
      Z14,179.754,179.75
      Z2262,500262,500
      Z3807807
      |L|2222
      Z−0.97838−0.98298

      Table 5. 

      Objective function optimization results with ds = 150.

    • Origin index Destination index
      Zone 001 Zone 002 Zone 003 Zone 004 Zone 005
      Zone 001 − 300 500 300 500
      Zone 002 500 − 500 300 500
      Zone 003 500 300 − 300 500
      Zone 004 500 300 500 − 500
      Zone 005 500 300 500 500 −

      Table 6. 

      OD matrix of social vehicles (unit: vehicles).